Question

for any answers with a square root, write your answer in the form sqrt(__) with no spaces.
find the length of each segment.
fe =
ed =
fd =

Explanation:

Identify coordinates of points

Identify coordinates from the grid.
The origin \((0,0)\) is marked.
Each grid line represents \(1\) unit.
Point \(D\) is at \((-1, 0)\).
Point \(E\) is at \((-3, 5)\).
Point \(F\) is at \((-5, 5)\).

Calculate length of FE

Find horizontal distance between points.
Since \(F\) and \(E\) share the same y-coordinate:

$$FE = |-3 - (-5)| = 2$$

Calculate length of ED

Apply the distance formula.
Using coordinates \(E(-3, 5)\) and \(D(-1, 0)\):

$$ED = \sqrt{(-1 - (-3))^2 + (0 - 5)^2}$$

$$ED = \sqrt{2^2 + (-5)^2} = \sqrt{4 + 25} = \sqrt{29}$$

Calculate length of FD

Apply the distance formula.
Using coordinates \(F(-5, 5)\) and \(D(-1, 0)\):

$$FD = \sqrt{(-1 - (-5))^2 + (0 - 5)^2}$$

$$FD = \sqrt{4^2 + (-5)^2} = \sqrt{16 + 25} = \sqrt{41}$$

Answer:

Question 1

Find the length of each segment.
\(FE =\) <blank>2</blank>

Question 2

\(ED =\) <blank>sqrt(29)</blank>

Question 3

\(FD =\) <blank>sqrt(41)</blank>